Transcript 6.4 Use Inscribed Angles and Polygons

6.4
Use Inscribed Angles and
Polygons
6.3-6.4 Quiz: Friday
Vocabulary
• An inscribed angle is an angle whose
vertex is on the circle and whose sides
contain chords of the circle.
Vocabulary
• The arc that lies in the interior of an
inscribed angles and has endpoints on the
angle is called the intercepted arc of the
angle.
Vocabulary
• Measure of an Inscribed Angle Theorem
– the measure of an inscribed angle is one half the
measure of its intercepted arc.
A
100o
B
50o
C
Vocabulary
• Theorem 6.10
– If two inscribed angles of a circle intercept the
same arc, then the angles are congruent.
Vocabulary
• A polygon is an inscribed polygon if all of
its vertices lie on a circle. The circle that
contains the vertices is a circumscribed
circle.
– Remember: a polygon is a closed figure made up of 3 or
more straight lines.
Vocabulary
• Theorem 6.11
– If a right triangle is inscribed in a circle, then
the hypotenuse is a diameter of the circle.
Vocabulary
• Theorem 6.12
– A quadrilateral (4-sided figure) can be
inscribed in a circle if and only if its opposite
angles are supplementary (add up to be 180o)
90O
90O
Example:
• Find the indicated measure in circle P.
a) angle S
b) arc RQ
You Try:
Example:
• Find the value of each variable.
You Try:
• Find the values of a and b.
Classwork/Homework
• P. 207 #1 – 18